Dynamics_Part37

Dynamics_Part37 - Since the ball starts from rest, we know...

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Since the ball starts from rest, we know that T 1 =0 . Also, setting the origin of our coordinate system at the ground, we have 0+ mg ( H + h )= 1 2 mV 2 + mgh Solving for V gives V = 0 2 gH Since the initial velocity of the ball is v = V k , there follows v t = t · v = V sin β v n = n · v = V cos β Turning to the impact between ball and the incline, the tangential velocity component is unchanged, which tells us that v I t = V sin β where v I = v I n n + v I t t is the ball’s velocity just after the impact. The impact relation tells us that since the coefficient of restitution is e , and since the incline is immovable, 0 v I n = e ( v n 0) = v I n = ev n = eV cos β Hence, just after the impact, the ball’s velocity is v I = eV cos β n + V sin β t Substituting for n and t from above, we have v I = eV cos β ( i sin β + k cos β )+ V sin β ( i cos β k sin β ) =( eV sin β cos β + V sin β cos β ) i + D eV cos 2 β V sin 2 β i k Making use of the following trigonometric identities sin β cos β
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